ECM1108
Fluid Mechanics Coursework
590025790
Impact of a Jet
Introduction
Using an Armfield F1-10 hydraulic bench, the force of a jet that impacts onto a target plate
can be investigated. These reaction forces are produced from the change in momentum. It
is expected the greater the momentum transfer, the greater the mass required to balance the
plate and jet.
Method
Apparatus
 Armfield F1-10 hydraulic bench
 F1-16 equipment
 Stopwatch
Set-Up
Using four different types of deflector angle (30, 90,120,180 degrees), masses are applied to
a plate upon which a water jet is impacting, until the system behaves in equilibrium. The
base plate is known to be in equilibrium when the target plate is raised vertically by the
impacting water until the weight pan reaches the level
gauge as shown in figure one.
During this time a reading of the amount of water
flowing is required and found by taking a measurement
from the sight glass. The volume of water
accumulated is in litres and is converted to metres
cubed using the conversion factor: 1 litre = 0.001
metres cubed.
To find the volumetric flow rate, the time period of the
collection of the water is also taken using the
stopwatch.
This process is repeated for each of the four deflector
plates. Altering the valve which controls the flow rate
into the apparatus allows the experiment to be
undertaken again to obtain at least two sets of data.
Figure 1- Impact of a jet experiment set up
The data can be processed to obtain relevant information that can be compared to the
known theoretical data.
Graphically representing the results also will show how accurate the experimental data is.
The gradient of the theoretical data is obtained from a regression line and this is compared
to the value from:
ECM1108
Fluid Mechanics Coursework
590025790
equation 1: 𝑠 = 𝜌𝐴(𝑐𝑜𝑠𝜃 + 1)
Results
From the four raw data items obtained from the experiment (deflector angle, volume
collected in litres, time to collect, and the mass applied) and using known formulae the mass
applied and velocity squared values can be used to represent the results graphically.
flow rate
1
flow rate
2
Nozzle
Deflector Deflector Volume Volume Time
Mass
Diameter
Type
Type
Applied W
(m)
(degrees) (radians)
(L)
(m³)
(s)
(Kg)
0.008
30
0.523599
3
0.003
8.69
0.070
0.008
90
1.570796
3
0.003
7.94
0.350
0.008
120
2.094395
3
0.003
7.94
0.550
0.008
180
3.141593
3
0.003
7.43
0.660
0.008
30
0.523599
1
0.001 17.28
0.020
0.008
90
1.570796
2
0.002 11.47
0.090
0.008
120
2.094395
2
0.002
9.72
0.140
0.008
180
3.141593
2
0.002 10.21
0.150
Flow Rate (Qt) Velocity
(m³/ s)
0.000345224
0.000377834
0.000377834
0.000403769
5.78704E-05
0.000174368
0.000205761
0.000195886
(m/s)
6.868021
7.516764
7.516764
8.032719
1.151294
3.468939
4.093491
3.897036
veloctity²
(m/s)²
47.1697143
56.5017363
56.5017363
64.52457775
1.325478883
12.03354108
16.75667131
15.18688822
Flow Rate
Qt
(m³/s)
0.3452244
0.3778338
0.3778338
0.4037685
0.0578704
0.1743679
0.2057613
0.1958864
Force
(N)
0.6867
3.4335
5.3955
6.4746
0.1962
0.8829
1.3734
1.4715
Calculated
slope from
experiment
0.0107
0.0574
0.1012
0.1014
0.0107
0.0574
0.1012
0.1014
calculated
slope from
theory
0.006734298
0.050265482
0.075398224
0.100530965
0.006734298
0.050265482
0.075398224
0.100530965
Table 1 – Data collected
Table 1 shows the collected and calculated data from the experiment. Included in this table
is a calculation of accuracy in percentage compared to the theoretical slope.
Figure 2 – All of the experimental data plotted on the same axis
calculated
error
%
58.88813432
14.19367167
34.22066867
0.864445184
58.88813432
14.19367167
34.22066867
0.864445184
ECM1108
Fluid Mechanics Coursework
590025790
Graphical comparison of the experimental and theoretical data
Figure three shows the comparison
of the line of the theoretical data
compared to the experimental.
The y-axis intercept is not important
in this as there would be other
coefficients involved.
The stronger the experimental data
is, the more parallel it would be to
the theoretical.
Figure 3- 30 degrees deflector
Figure four shows the same details
as the previous deflector plate.
Figure 4 – 90 degrees deflector
Figure five shows the divergence of
the experimental and theoretical
data.
Figure 5 – 120 degrees deflector
ECM1108
Fluid Mechanics Coursework
590025790
Figure 6 shows the parallel lines
on top of each other which are
near perfect.
Figure 6 -180 degrees deflector
Conclusion
Error
The average human reaction time to light stimuli is 19ms (0.19 seconds) [2]. This combined
with imprecise measurements of the collection of the water has an affect on the accuracy of
the results. An estimation of this effect is likely to be a ± 0.1L error
When balancing the impact of the jet with the mass applied, the weights are supplied in a set
with the lowest weight 10 grams. A load of 55 grams for example, would not be possible.
This too has increased the inaccuracy of the results by ± 0.01 Kg.
Calculating the error values for velocity squared and applied mass taking into account these
errors is shown in table 2. Table 3 (see appendix) is the full table of calculations of the error.
Deflector
ERROR %
Type
(degrees) veloctity² Force
30
2.257342 14.28571
flow rate
90
1.845253 2.857143
1
120
1.845253 1.818182
180
1.519288 1.515152
30
18.38237
50
flow rate
90
6.686221 11.11111
2
120
6.062979 7.142857
180
6.258432 6.666667
Where there was a much lower flow rate (flow rate
two) and using the thirty degree deflection plate,
the error was abnormally higher and was
anomalous to the other data (highlighted).
Generally where the forces and velocities were
higher the percentage of error was lower. Using
the error percentage for the flow rate two and
applying these as error bars to the graph provides
a more accurate representation.These are the
error bars that are used:
Table 2 –Error calculations
Deflection angle (degrees)
30
90
120
180
Table 3- Error bars
Horizontal error bar (±%)
18
7
6
6
Vertical error bar (±%)
50
11
7
7
ECM1108
Fluid Mechanics Coursework
590025790
Figure 7 – Collective data as (figure 2) with calculated error bars.
Discussions
Taking more readings of more flow rates would make a stronger result set. Also repeating
the experiment more times the flow rates one and two to get data which averages could be
taken would improve the accuracy further than in figure 7.
References
[1] - http://www.discoverarmfield.co.uk/data/f1/images/f1_16_rgb.jpg
[2] - http://biae.clemson.edu/bpc/bp/Lab/110/reaction.htm#Type%20of%20Stimulus , 1st line ,
“Mean Reaction Times” paragraph.
Appendix
Nozzle Deflector Deflector Volume
Diameter Type
Type
(m)
(degrees) (radians)
(L)
0.008
30
0.523599
3
0.008
90
1.570796
3
0.008
120
2.094395
3
0.008
180
3.141593
3
0.008
30
0.523599
1
0.008
90
1.570796
2
0.008
120
2.094395
2
0.008
180
3.141593
2
new
Volume
volume
(L)
(m³)
3.1
0.003
3.1
0.003
3.1
0.003
3.1
0.003
1.1
0.001
2.1
0.002
2.1
0.002
2.1
0.002
0.0031
0.0031
0.0031
0.0031
0.0011
0.0021
0.0021
0.0021
Time
Time +.19
(s)
8.69
7.94
7.94
7.43
17.28
11.47
9.72
10.21
(s)
8.88
8.13
8.13
7.62
17.47
11.66
9.91
10.4
Table 4 – Full table of results calculating the error
Mass
Applied W
(Kg)
0.070
0.350
0.550
0.660
0.020
0.090
0.140
0.150
Mass
10
0.080
0.360
0.560
0.670
0.030
0.100
0.150
0.160
Flow Rate (Qt) Velocity veloctity²
(m³/ s)
0.000349099
0.000381304
0.000381304
0.000406824
6.29651E-05
0.000180103
0.000211907
0.000201923
(m/s)
6.945106
7.585798
7.585798
8.093509
1.252651
3.583034
4.215759
4.017132
(m/s)²
48.2345
57.54434
57.54434
65.50489
1.569133
12.83813
17.77262
16.13735
Force
(N)
0.7848
3.5316
5.4936
6.5727
0.2943
0.981
1.4715
1.5696
Calculated
slope from
experiment
0.0107
0.0574
0.1012
0.1014
0.0107
0.0574
0.1012
0.1014
calculated
slope from
theory
0.0067343
0.0502655
0.0753982
0.100531
0.0067343
0.0502655
0.0753982
0.100531